The burden of these remarks is that, from the point of view of the CEP, a slow roll inflationary model naturally ends up as a dilute gas of black holes whose Schwarzschild radius coincides with the inflationary horizon size, as long as the universe expands fast enough for the black holes to avoid merging into a single horizon filling hole. We'll call these Inflationary Black Holes, IBHs. It's important to emphasize that the inflationary scalar field is, in this view, an artificial construct.
One starts with a scale factor \(a(t) =\sinh ^{1/3} (3 H(t) t) \)  with \(\epsilon \equiv \frac{\dot{H}}{H^2} \)  small and defines \(p\)  and \(\rho \)  from the Friedmann equation. The underlying quantum model is not a quantum field theory but a system with a time dependentAs discussed above, time dependence is forced on us by our choice of cosmological Milne coordinates, as well as by the implementation of causality without quantum field theory. Hamiltonian in a finite dimensional Hilbert space. The growth of the size of the diamond Hilbert space with proper time, determines the slow roll geometry. However, if \(p + \rho \ge 0\)  then we can find a scalar field Lagrangian whose classical dynamics maps out the same geometry. The null energy condition is just the statement[1]} that entropy is always increasing. In the underlying quantum dynamics this occurs simply because more degrees of freedom are coupled to the system as DU time increases.
